“Men/People may doubt what you say, but they will (always) believe what you do” means that actions count for more than just talk. The saying has been credited to American military officer and politician Lewis Cass (1782-1866), but there is no evidence that he said it.
 
British Baptist preacher Charles Haddon Spurgeon (1834-1892) wrote “Men may doubt what you say, but they will believe what you do” in his book Feathers for Arrows (1870). Other sources in the 1870s-1880s also credited Spurgeon for the saying.
 
“Don’t tell people your plans. Show them your results” is a similar saying.
 
       
Wikipedia: Charles Spurgeon
Charles Haddon (C.H.) Spurgeon (June 19, 1834 – January 31, 1892) was a British Particular Baptist preacher who remains highly influential among Christians of different denominations, among whom he is still known as the “Prince of Preachers.” This despite the fact that he was a strong figure in the Reformed Baptist tradition, defending the Church in agreement with the 1689 London Baptist Confession of Faith understanding, against liberalism and pragmatic theological tendencies even in his day.
 
In his lifetime, Spurgeon preached to around 10,000,000 people, often up to 10 times each week at different places. His sermons have been translated into many languages. Spurgeon was the pastor of the congregation of the New Park Street Chapel (later the Metropolitan Tabernacle) in London for 38 years. He was part of several controversies with the Baptist Union of Great Britain and later had to leave that denomination. In 1857, he started a charity organization called Spurgeon’s which now works globally. He also founded Spurgeon’s College, which was named after him posthumously.
 
Spurgeon was a prolific author of many types of works including sermons, an autobiography, a commentary, books on prayer, a devotional, a magazine, poetry, hymnist, and more. Many sermons were transcribed as he spoke and were translated into many languages during his lifetime. Arguably, no other author, Christian or otherwise, has more material in print than C.H. Spurgeon.
 
Wikipedia: Lewis Cass
Lewis Cass (October 9, 1782 – June 17, 1866) was an American military officer and politician. During his long political career, Cass served as a governor of the Michigan Territory, an American ambassador, and a U.S. Senator representing Michigan. He was the nominee of the Democratic Party for President of the United States in 1848 and a leading supporter of the Doctrine of Popular Sovereignty, which would have allowed indidividual states to determine whether to make slavery legal instead of entirely restricting its expansion.
 
ThinkExist.com
“People may doubt what you say, but they will believe what you do.”
Lewis Cass quotes
     
Google Books
Feathers for arrows: or, Illustrations for preachers and teachers, from my note book
By C. H. Spurgeon
New York, NY: Fleming H. Revell
1870
Pg. 131:
Men may doubt what you say, but they will believe what you do.
 
Google Books
The Christian pioneer
Edited by Joseph Foulkes Winks
Volume 28
1874
Pg. 242:
Men may doubt what you say, but they will believe what you do.
     
Google Books
The Biblical illustrator; or, Anecdotes, similes emblems, illustrations; expository, scientific, geographical, historical, and homiletic, gathered from a wide range of home and foreign literature, on the verses of the Bible,
By Joseph S. Exell
New York, NY: Fleming H. Revell Co.
1887
Pg. 320:
Men may doubt what you say, but they wUl believe what you do. (C. H. Spurgeon.)
 
Google Books
Dictionary of anecdote, incident, illustrative fact, selected and arranged for the pulpit and the platform
By Walter Baxendale
New York, T. Whittaker
1888
Pg. 353, col. 1:
Men may doubt what you say, but they will believe what yon do. — Spurgeon.
 
10 April 1938, Florecne (SC) Morning News, “For the Scrap Book,” pg. 4, col. 5:
Men may doubt what you say, but they will believe what you do.—Anon.
 
Google News Archive
10 March 1960, Beaver County (PA) Times, “Daily Diet Of Detail,” pg. 6, col. 6:
People may doubt what you say, but they will always believe what you do.
 
Google Books
The Reader’s digest
v. 113 - 1978
Pg. 127:
Men may doubt what you say, but they will believe what you do.
—Lewis Cass